Orthogonal $F$-weak Contraction Mapping in Orthogonal Metric Space, Fixed Points and Applications

Abstract

In the present article, we introduce the concept of orthogonal $F$-weak contraction mapping in an orthogonal metric space along with some fixed point results in this setting. Also, the example given in the main result shows that the result proved in this article is a proper extension of some of the results present in the literature. As an application, the main results are applied to prove the existence and uniqueness of the solution for first order differential equation.